In sports racktet frame, such as tennis racket, the design goal is to have the highest in strength to weight ratio, and the lowest in cost. Materials have been changed from wood to metal and progressed to fiber reinforced plastics, with sizes from small to large to medium plus heads, which all contribute to better rackets. But the cost of production remains high due to the complicated process of modern fiber reinforced composite technology. The frame of a fiber reinforced racket is usually of a hollow, thin-walled cross section with a large number of fiber/thermoplastic layers piled one layer over the other at different fiber orientation angles for optimum strength. The steps of cutting multi-layered cloth, folding the same over thermo-expandable core or air tube, laying into the mold, heat treating, polishing and adding cosmetics, are all very time-consuming and labor intensive. Hence the high production cost of modern fiber-reinforced rackets.
The main difficulty in racket frame design technology is the extreme high ratio of the strength to weight required. This explains why people in the trade maintain the existing practice and refuse to acknowledge new approaches. For example, the weight of a tennis racket is from 335 gm to 370 gm, with about 350 grams, preferred by most players, as nominal. Within the 350 grams, bumper guard plus the grommet strips take 22 gm, handle foams 27 gm, leather grip 17 gm, end cap 10 gm, string 21 gm, and polishing plaster and paint 19 gm, with the composite frame extending from the head to the end being about 232 gm. The mass allocated to form the portion of the frame to support the string network from the head of the racket to the throat, measured about 80 cm in circumference, is about 100 gm. To apportion more material from the rear part of the frame to the ball-playing area will make the tennis racket too head-heavy for most players. The 100 grams distributed to a length of 80 cm is approximately 1.25 gm per centimeter (0.11 oz per inch). If the material is 100% graphite/epoxy which has a specific gravity of 1.35, the 1.25 gm/cm will yield an average volume density of 0.90 c.c. volume for each centimeter of the circumference along the ball-hitting region. This is the goal of frame design.
However, for that allocated little mass per unit length, a great deal of load-carrying capacity is expected. Each string is pre-stressed at over 65 pounds of force. At a circumference of 80 centimeters, excluding the throat length, there are 16 such highly loaded longitudinal strings and 20 cross strings. The cross section of the frame should be strong enough to serve the tennis ball at a speed over 120 miles per hour for many hours of play without failure. Even the aluminum alloy is presently thought of as too heavy to achieve the desired weight distribution (Volume density) at the head.
A high performance racket with composite material may achieve the design goal but the frame should vary optimally in height and width along the periphery of the network area, along the throat, the shank, and into the handle. An optimum design for fiber reinforced frame has to have the necessary dimension at a particular location to resist the load. It needs an average bending moment of inertia (l.sub.x) of about 0.28 cm.sup.4 with respect to the x-axis, parallel to the string network plane, to resist the ball force, and a bending moment of inertia (l.sub.y) of about 0.08 cm.sup.4 with respect to the y-axis, perpendicular to the string network plane, to resist the stringing load. A sufficient polar moment of inertia for the cross section is also required. Consequently, a labor intensive molding method is best suited for fabricating the modern fiber-reinforced tennis rackets, because it can be manipulated in width and in height, and in varying numbers of layers and in reinforcing patches, to achieve the maximum strength with minimum weight. This is the main reason that people in the trade never have given serious thoughts to consider other fabrication methods, and other frame shapes than the time tested thin-walled, hollow frame. These professionals have been constantly exposed to other feasible production processes in other industries and in other products. Most of the innovative ideas published are not practical to meet the rigorous strength to weight requirement and they all are inferior to the graphite thin walled hollow frame. A new invention to suggest a different frame should pass the criteria that it can have, or even better, the required sectional properties listed before as achieved by prior art and show it can be superior in simplicity and in cost.